Approaches To The Qualitative Theory Of Ordinary Differential Equations Dynamical Systems And Nonlinear Oscillations
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Approaches To The Qualitative Theory Of Ordinary Differential Equations
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Author : Tong-ren Ding
language : en
Publisher:
Release Date : 2007
Approaches To The Qualitative Theory Of Ordinary Differential Equations written by Tong-ren Ding and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.
Approaches To The Qualitative Theory Of Ordinary Differential Equations Dynamical Systems And Nonlinear Oscillations
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Author : Tong-ren Ding
language : en
Publisher: World Scientific Publishing Company
Release Date : 2007-08-13
Approaches To The Qualitative Theory Of Ordinary Differential Equations Dynamical Systems And Nonlinear Oscillations written by Tong-ren Ding and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-13 with Mathematics categories.
This book is an ideal text for advanced undergraduate students and graduate students with an interest in the qualitative theory of ordinary differential equations and dynamical systems. Elementary knowledge is emphasized by the detailed discussions on the fundamental theorems of the Cauchy problem, fixed-point theorems (especially the twist theorems), the principal idea of dynamical systems, the nonlinear oscillation of Duffing's equation, and some special analyses of particular differential equations. It also contains the latest research by the author as an integral part of the book.
Methods Of Qualitative Theory In Nonlinear Dynamics
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Author : Leonid P. Shilnikov
language : en
Publisher: World Scientific
Release Date : 1998
Methods Of Qualitative Theory In Nonlinear Dynamics written by Leonid P. Shilnikov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Science categories.
Bifurcation and Chaos has dominated research in nonlinear dynamics for over two decades and numerous introductory and advanced books have been published on this subject. There remains, however, a dire need for a textbook which provides a pedagogically appealing yet rigorous mathematical bridge between these two disparate levels of exposition. This book is written to serve the above unfulfilled need. Following the footsteps of Poincare, and the renowned Andronov school of nonlinear oscillations, this book focuses on the qualitative study of high-dimensional nonlinear dynamical systems. Many of the qualitative methods and tools presented in this book were developed only recently and have not yet appeared in a textbook form. In keeping with the self-contained nature of this book, all topics are developed with an introductory background and complete mathematical rigor. Generously illustrated and written with a high level of exposition, this book will appeal to both beginners and advanced studentsof nonlinear dynamics interested in learning a rigorous mathematical foundation of this fascinating subject.
Nonlinear Differential Equations And Dynamical Systems
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Author : Ferdinand Verhulst
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Differential Equations And Dynamical Systems written by Ferdinand Verhulst and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
For lecture courses that cover the classical theory of nonlinear differential equations associated with Poincare and Lyapunov and introduce the student to the ideas of bifurcation theory and chaos, this text is ideal. Its excellent pedagogical style typically consists of an insightful overview followed by theorems, illustrative examples, and exercises.
The Qualitative Theory Of Ordinary Differential Equations
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Author : Fred Brauer
language : en
Publisher: Courier Corporation
Release Date : 2012-12-11
The Qualitative Theory Of Ordinary Differential Equations written by Fred Brauer and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-11 with Mathematics categories.
Superb, self-contained graduate-level text covers standard theorems concerning linear systems, existence and uniqueness of solutions, and dependence on parameters. Focuses on stability theory and its applications to oscillation phenomena, self-excited oscillations, more. Includes exercises.
Qualitative Theory Of Odes An Introduction To Dynamical Systems Theory
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Author : Henryk Zoladek
language : en
Publisher: World Scientific
Release Date : 2022-10-21
Qualitative Theory Of Odes An Introduction To Dynamical Systems Theory written by Henryk Zoladek and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-21 with Mathematics categories.
The Qualitative Theory of Ordinary Differential Equations (ODEs) occupies a rather special position both in Applied and Theoretical Mathematics. On the one hand, it is a continuation of the standard course on ODEs. On the other hand, it is an introduction to Dynamical Systems, one of the main mathematical disciplines in recent decades. Moreover, it turns out to be very useful for graduates when they encounter differential equations in their work; usually those equations are very complicated and cannot be solved by standard methods.The main idea of the qualitative analysis of differential equations is to be able to say something about the behavior of solutions of the equations, without solving them explicitly. Therefore, in the first place such properties like the stability of solutions stand out. It is the stability with respect to changes in the initial conditions of the problem. Note that, even with the numerical approach to differential equations, all calculations are subject to a certain inevitable error. Therefore, it is desirable that the asymptotic behavior of the solutions is insensitive to perturbations of the initial state.Each chapter contains a series of problems (with varying degrees of difficulty) and a self-respecting student should solve them. This book is based on Raul Murillo's translation of Henryk Żołądek's lecture notes, which were in Polish and edited in the portal Matematyka Stosowana (Applied Mathematics) in the University of Warsaw.
Nonlinear Dynamical Systems In Engineering
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Author : Vasile Marinca
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-05
Nonlinear Dynamical Systems In Engineering written by Vasile Marinca and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-05 with Technology & Engineering categories.
This book presents and extend different known methods to solve different types of strong nonlinearities encountered by engineering systems. A better knowledge of the classical methods presented in the first part lead to a better choice of the so-called “base functions”. These are absolutely necessary to obtain the auxiliary functions involved in the optimal approaches which are presented in the second part. Every chapter introduces a distinct approximate method applicable to nonlinear dynamical systems. Each approximate analytical approach is accompanied by representative examples related to nonlinear dynamical systems from to various fields of engineering.
Dynamical Systems And Chaos
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Author : Henk Broer
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-20
Dynamical Systems And Chaos written by Henk Broer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-20 with Mathematics categories.
Over the last four decades there has been extensive development in the theory of dynamical systems. This book aims at a wide audience where the first four chapters have been used for an undergraduate course in Dynamical Systems. Material from the last two chapters and from the appendices has been used quite a lot for master and PhD courses. All chapters are concluded by an exercise section. The book is also directed towards researchers, where one of the challenges is to help applied researchers acquire background for a better understanding of the data that computer simulation or experiment may provide them with the development of the theory.
Mathematical Modeling
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Author : Antonio Palacios
language : en
Publisher: Springer Nature
Release Date : 2022-09-19
Mathematical Modeling written by Antonio Palacios and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-19 with Technology & Engineering categories.
This book provides qualitative and quantitative methods to analyze and better understand phenomena that change in space and time. An innovative approach is to incorporate ideas and methods from dynamical systems and equivariant bifurcation theory to model, analyze and predict the behavior of mathematical models. In addition, real-life data is incorporated in the derivation of certain models. For instance, the model for a fluxgate magnetometer includes experiments in support of the model. The book is intended for interdisciplinary scientists in STEM fields, who might be interested in learning the skills to derive a mathematical representation for explaining the evolution of a real system. Overall, the book could be adapted in undergraduate- and postgraduate-level courses, with students from various STEM fields, including: mathematics, physics, engineering and biology.
Perturbation Methods In Non Linear Systems
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Author : Georgio Eugenio Oscare Giacaglia
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Perturbation Methods In Non Linear Systems written by Georgio Eugenio Oscare Giacaglia and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This volume is intended to provide a comprehensive treatment of recent developments in methods of perturbation for nonlinear systems of ordinary differ ential equations. In this respect, it appears to be a unique work. The main goal is to describe perturbation techniques, discuss their ad vantages and limitations and give some examples. The approach is founded on analytical and numerical methods of nonlinear mechanics. Attention has been given to the extension of methods to high orders of approximation, required now by the increased accuracy of measurements in all fields of science and technology. The main theorems relevant to each perturbation technique are outlined, but they only provide a foundation and are not the objective of these notes. Each chapter concludes with a detailed survey of the pertinent literature, supplemental information and more examples to complement the text, when necessary, for better comprehension. The references are intended to provide a guide for background information and for the reader who wishes to analyze any particular point in more detail. The main sources referenced are in the fields of differential equations, nonlinear oscillations and celestial mechanics. Thanks are due to Katherine MacDougall and Sandra Spinacci for their patience and competence in typing these notes. Partial support from the Mathematics Program of the Office of Naval Research is gratefully acknowledged.